R-squared (R2) measures how well a regression model fits the data. It tells you what percentage of the variation in the outcome (dependent variable) is explained by the factors you are studying (independent variables).
For example, if the value of is,(R2) ,0.8 (or 80%), it means 80% of the changes in the outcome can be explained by your model, and the remaining 20% is due to other factors that are not included.
The R-squared metric, expressed as a percentage between 0 and 100, helps gauge this relationship. An R-squared of 100 indicates the fund's performance mirrors the benchmark perfectly, while a lower number suggests the fund's ups and downs are less reliant on the benchmark's movements.
So, let us examine the meaning and significance of the R-squared metric, how it is calculated and what its limitations are.
What is R-Squared?
In statistical terms, R-squared (also known as the coefficient of determination) measures the variance in a dependent variable with respect to an independent variable. This metric is derived from the regression model and is distinct from the correlation of an asset.
The correlation tells you how strongly one variable depends on another. However, the R-squared evaluates how the variance in one variable can be explained using the variance of another variable. For instance, every mutual fund scheme has a corresponding benchmark. The R-squared of a mutual fund with respect to its benchmark index tells you how much the fund’s performance mirrors the benchmark and is affected by it..
How does R-Squared work?
R-squared is a statistical measure (usually between 0 and 100) that helps assess how closely a mutual fund's performance mirrors its benchmark index. It essentially reflects the connection between the fund’s returns and the index's returns. While calculating R-squared involves several steps, most online platforms conveniently display the value on the fund information page.
In simpler terms, R-squared uses variations within the data to determine the strength of the relationship. There is no need to perform complex calculations yourself – most brokers provide the R-squared value readily available.
To find a mutual fund that closely tracks its benchmark, look for the R-squared value (often denoted as "R2") on the fund's information page.
Here's a general breakdown of R-squared categories:
- Low correlation (1-40%): The fund's performance has a weak link to the benchmark.
- Average correlation (41-70%): The fund's performance somewhat aligns with the benchmark.
- High correlation (71-100%): The fund's performance closely mirrors the benchmark.
The choice of R-squared depends on your investment goals. If you prefer a fund that behaves similarly to the benchmark, you’d target a higher R-squared, ideally above 90%.
R-Squared formula and calculating the value
The process of calculating the R-squared value for mutual funds and other assets can be quite time-consuming. The formula, as shown below, is quite straightforward. However, finding the metrics used in the formula can be tedious.
| R-squared = 1 — (Unexplained variation ÷ Total variation |
To calculate the unexplained variation, you need to follow the steps outlined below:
- Use the data points of the dependent and independent variables to find the line of best fit.
- Then, find the difference between the predicted values and the actual values.
- Square the difference obtained above and add all the differences to get the total of errors squared.
- This is the unexplained variation.
To find the total variation:
- Find the difference between each actual value and the average value.
- Square each of the above differences and add them.
Needless to say, this can be prone to errors and time-consuming if you are investing in a volatile market. A better alternative to calculate the R-squared is to use the formula given below in a excel spreadsheet:
| R-squared = RSQ ([Data set 1],[Data set 2]) |
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Interpret R-Squared values in investing
R-squared is typically expressed as a percentage and its value can range from 0% to 100%. The higher the value, the more the dependent variable’s variation can be explained by the variation of the independent variable.
For instance, take the case of a mutual fund and its benchmark. The fund is the dependent variable here, and the benchmark is the independent variable. A 70% R-squared in the mutual fund means that the benchmark’s variation accounts for only 70% of the mutual fund’s variation. The remaining 30% is due to other non-benchmark-related factors.
How to read an R-Squared for a fund?
A higher R-squared indicates a stronger correlation between the fund and its benchmark, implying that a significant portion of the mutual fund portfolio mirrors the benchmark's movements. Conversely, a lower R-squared suggests less reliance on the benchmark. However, a lower R-squared doesn't necessarily imply poor performance; it varies based on the fund type.
For instance, index funds aim to closely track the benchmark, resulting in naturally high R-squared values. Conversely, other equity funds may have lower R-squared values as they strive to outperform the benchmark without strictly replicating its portfolio. A 100% R-squared would signify that the benchmark entirely explains the portfolio's performance.
How is the value of R-Squared in mutual funds useful?
The R-squared value can be used to choose the right kind of investment for your portfolio. If you want to mimic the returns or performance of a benchmark index, for instance, you must compare mutual funds and choose those where the R-squared value is very high — preferably 95% or more.
You can find such high R-squared in index funds, which are specifically designed to mimic the movement of the benchmark index. Other funds that are actively managed may have lower R-squared values.
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Drawbacks of the R-Squared measure
The R-squared values can be useful to measure an asset against its benchmark. However, it falls short in other areas, as outlined below:
- It relies on historical data, which may not repeat itself.
- It does not facilitate comparison with other investments.
- It cannot help you measure the performance of an asset.
Tips for improving R-squared
Improving R-squared refers to the process of fine-tuning the model. It is usually done by carefully selecting the right predictors (independent variables). Be aware that not all variables contribute equally to explaining the outcome, so identifying and using only the most relevant ones can boost R-squared.
Mostly, this requires thorough analysis, like examining data trends and relationships or using techniques like stepwise regression, where variables are added or removed based on their impact on the model. It is worth mentioning that the ultimate goal is to include variables that genuinely help explain the outcome while avoiding those that add noise or confusion.
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Another important aspect related to fine-tuning is addressing “multicollinearity”. It occurs when independent variables are too closely related to each other. When this happens, it usually distorts the model's accuracy and makes the results less reliable.
Now, to tackle this, you can use these methods:
- Perform Variance inflation factor (VIF) analysis to detect multicollinearity
or - Apply principal component analysis (PCA) to reduce the correlation between variables.
It must be noted that by managing multicollinearity, you can improve the clarity of the model and, in a way, improve R-squared.
Additionally, you can also refine the model by exploring “nonlinear relationships” between variables. Sometimes, simple linear relationships don't capture the true nature of the data. Hence, to better capture the underlying patterns in the data, you can consider the following:
- Higher-order terms (like squares or cubes of variables)
- Interactions between variables, or
- Transforming variables (like taking the log or square root).
However, be aware that this approach requires deep knowledge of the subject area. Only then can you identify the most meaningful transformations.
Adjusted R-Squared: An effective alternative
The R-squared is also limiting because it can only account for one independent variable or benchmark. However, most assets and mutual funds may have more than one benchmark. An adjusted R-squared can help you measure the impact of multiple independent variables or benchmarks on an asset.
To put it simply, the R-squared value always increases when more variables are added. But this increase may not necessarily translate to a rising correlation. An adjusted R-squared, however, can help you figure out the impact of different benchmarks more accurately.
R-squared vs. Adjusted R-squared
While R-squared is a helpful metric, it has limitations. It can be overly sensitive to the number of assets in a mutual fund, particularly for funds with smaller portfolios. This can lead to a misleading interpretation of the correlation between the fund and its benchmark.
To address this limitation, another statistical measure called adjusted R-squared is introduced. Adjusted R-squared penalises the model for adding more explanatory variables (assets) to the equation. In simpler terms, it adjusts for the complexity of the model.
Here's a quick comparison:
- R-Squared: Simpler to calculate, but can be inflated by the number of assets in the fund.
- Adjusted R-Squared: More nuanced, penalises for model complexity, offering a potentially more accurate picture of the correlation.
While both metrics provide valuable insights, adjusted R-squared is generally considered a more reliable indicator of the true relationship between a mutual fund and its benchmark, particularly for funds with a large number of holdings.
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When to use each metric?
- R-Squared: A good starting point for a quick assessment, especially for funds with a limited number of holdings.
- Adjusted R-Squared: Preferred for a more precise analysis, particularly for funds with a larger and more diverse portfolio.
It is important to note that neither R-squared nor adjusted R-squared is a perfect measure. They should be used in conjunction with other investment research to make informed decisions about mutual funds.
How are R-squared and beta-related?
R-squared and Beta are two statistical tools. Both help investors understand the performance and risk of a mutual fund. When it comes to “Beta”, it measures the fund's volatility or how much its value fluctuates compared to a benchmark index (like the Nifty 50). A Beta of 1 means the fund's movements match the benchmark's movements. If Beta is above 1, the fund is more volatile than the benchmark, and if it’s below 1, it’s less volatile.
On the other hand, R-squared tells you how well the fund's movements are explained by the benchmark. A high R-squared means the fund's performance closely follows the benchmark, while a low R-squared indicates that the fund's performance is not well explained by the benchmark.
Moreover, it is worth mentioning that these two metrics are often used together. For example, say a fund has a high Beta (indicating high volatility) but a low R-squared. Now, this suggests that the fund's volatility may not be related to the benchmark. This also implies that relying solely on Beta could be misleading.
Therefore, by looking at both R-squared and Beta, investors get a clearer picture of how a fund performs in relation to its benchmark. Ultimately, this helps in making better-informed decisions.
Also read: What Is XIRR in Mutual Funds
Key Takeaways
- R-squared is a statistical measure ranging from 0 to 100 that reflects how closely a mutual fund's performance aligns with its benchmark index.
- A high R-squared (closer to 100) indicates the fund's performance closely mirrors the benchmark index.
- A low R-squared suggests the fund's ups and downs are less influenced by the benchmark's movements.
- Understanding R-squared helps investors assess how actively a fund is managed compared to passively following the benchmark.
- R-squared does not account for all factors affecting a fund's performance. Consider other aspects like expense ratio and investment philosophy before making investment decisions.
Conclusion
The R-squared is only one of the many factors you need to consider to evaluate an investment. Since the metric does not measure the performance of an asset or its broader market-related risk, you also need to look into other aspects like the asset’s beta, standard deviation and volatility. You can then make a more well-informed decision.
After you have performed the required analysis and identified the funds you want to invest in, you can visit the Bajaj Finserv Mutual Funds Platform and start your lump sum or SIP investment. With over 1,000 funds available to choose from, you are bound to find the funds that align with your risk preferences and financial goals.
